A few Pre-Calc problems in my AP Calc summer packet

Hey guys, my teacher said we could get help from anywhere and I figured this would be a good place.

1. Let f(x) = 2x-3 [x less than or equal to 2] and x^2 + a [x greater than 2]

Sketch the curve and find the value of "a" so that lim f(x) as x->2 = 1. I guess just find the value of "a"

2. A piece of cardboard measures 20 by 35 inches. Two equal squaares are removed from the corners of a 20 inch side. Two equal rectangles are removed from the other corners so that the tabs can be folded to form a rectangular box with a lid.

a. Write the forumla v(x) for the volume of the box.
b. Fidn the domain of V for this problem. Express in interval notation (don't worry about end points)
c. Find the maximum volume and the value of x that gives it. Justify your work.

3. Find the solution(s) for the following system. Express your answer correctly to three decimal places (use your calculator).

f(x)= (1/4) + sin((pi)(x))
g(x)= 4^(-x)

4. Let W(t) =95sqrt(t)(sin^2)(t/6). Find W(7) and W(10). For what value of "t" is W(t)= 0?

For the first one I graphed the 2x-3 part and have tried both positive and negative values for a. Nothing makes the limit as x approaches 2 = 1. Also, is there another way to solve it without graphing?

For #2, I know the height is equal to x. The width is equal to 20-2x. I don't know what to put for the last one. I put 35-x-y but it didn't work for me.

#3. I graphed it on my calculator. I need to look for where the two lines intersect, right?

#4. I've never seen a problem like this and I'm not the greatest at functions. So no, I haven't attempted this last one

Hey guys, my teacher said we could get help from anywhere and I figured this would be a good place.

1. Let f(x) = 2x-3 [x less than or equal to 2] and x^2 + a [x greater than 2]

Sketch the curve and find the value of "a" so that lim f(x) as x->2 = 1. I guess just find the value of "a"

With (2,1)

Originally Posted by INeedMathHelp33

2. A piece of cardboard measures 20 by 35 inches. Two equal squaares are removed from the corners of a 20 inch side. Two equal rectangles are removed from the other corners so that the tabs can be folded to form a rectangular box with a lid.

a. Write the forumla v(x) for the volume of the box.
b. Fidn the domain of V for this problem. Express in interval notation (don't worry about end points)
c. Find the maximum volume and the value of x that gives it. Justify your work.

I think you are looking for

Originally Posted by INeedMathHelp33

3. Find the solution(s) for the following system. Express your answer correctly to three decimal places (use your calculator).

f(x)= (1/4) + sin((pi)(x))
g(x)= 4^(-x)

Yep calculator is best for this one.

Originally Posted by INeedMathHelp33

4. Let W(t) =95sqrt(t)(sin^2)(t/6). Find W(7) and W(10). For what value of "t" is W(t)= 0?